Communication systems such as mobile telephone systems, internet connected computing devices, long distance communication lines, satellite systems, and other systems have had a profound effect on human development. Communication systems have made the world a smaller place by allowing people to communicate over great distances with relative ease. Mobile telephone systems have allowed people to be accessible and have access to data resources around the clock. These systems are relatively complicated and have many complementary components. As communication systems develop, there are increasing demands that the systems are designed to operate more efficiently and perform with increasing effectiveness. For example, mobile phones are expected to be able to transmit more data and have a minimized battery size.
In wireless communication systems, electrical data signals (e.g. voice signals, internet data, etc.) are transmitted from a transmitter to a receiver using antennas. In order for these electrical data signals to be propagated as radio waves with adequate strength, prior to the electrical data signals being propagated by an antenna, the electrical data signals need to be amplified by an amplifier. Amplifiers, particularly for high performing wireless devices, are relatively expensive and sensitive components. Accordingly, when a communication system is designed, cost and operation of an amplifier is carefully considered. For instance, if the amplifiers are too expensive, then a communication system cannot be constructed that is commercially viable. Likewise, if the amplifiers that are affordable for a communication system have inadequacies, then a communication system may not be functionally viable. As another example, if amplifiers implemented in battery operated devices (e.g. mobile telephones) are operated in an inefficient manner, then there may be undesirable battery drain, which could as a result undesirably increase the size and/or weight of the battery operated devices.
In communications systems, a relatively low power communication signal conveying data may be input into an amplifier and the amplifier may output a higher power communication signal. Although the relatively low power communication signal is inadequate to create radio waves through an antenna, the higher power communication signal may be propagated through an antenna so that communication is possible between two wireless devices. However, if the relatively low power communication signal input into the amplifier is too high, the amplifier will not operate properly, causing problems such as distortions or interference. If the relatively low power communication signals are too low, link data capacity is reduced or amplifier power efficiency may be non-optimal. Accordingly, in order to maximize the utility of an amplifier, the low power communication signal input into the amplifier should be as strong as possible relative to the signal magnitude threshold of an amplifier without the relatively low power communication signals exceeding the signal magnitude threshold of the amplifier. The signal magnitude threshold of an amplifier is related to the maximum signal strength that an amplifier can receive without causing distortions or interference.
Portions of the relatively low input communication signal input into an amplifier whose magnitude exceeds the signal magnitude threshold may be referred to as excursions. These excursions can be suppressed, thus allowing an amplifier to operate without distortions or interference or in an optimal power efficient manner. However, when these excursions are suppressed without frequency domain considerations, random noise at unacceptable levels may be introduced into the communication signal, which can unacceptably increase the rate of bit errors over the communication link. Many communication systems (e.g. LTE mobile phone communication systems) have performance requirements parameters, which constrain noise levels below certain levels relative to associated signal power. Accordingly, when excursions are suppressed, then these performance requirements parameters must also be satisfied.
Some communications systems are multipath communication systems where a transmitter has multiple antennas and a receiver has multiple antennas, which transmit and receive the same frequencies. Normally, competing signals transmitted and received using the same frequencies suffer from destructive interference. However, in multiple-in multiple-out (MIMO) communication systems or other multipath communication signals, the parallel signals can be strategically mixed together to manipulate the multipath radio environment. These mixed signals also have the challenge that they should not have excursions which exceed the signal magnitude thresholds of the associated amplifiers. Since these MIMO communication signals are a strategic mix of communication signals which may have different performance requirements parameters, it is a substantial challenge to compensate for these excursions while at the same time satisfying the performance requirements parameters of the communication system.
In some communication systems, cyclic prefixes are used in conjunction with modulation in order to retain sinusoids' properties in multipath channels. Sinusoidal signals are eigenfunctions of linear and time-invariant systems. Therefore, if the channel is assumed to be linear and time-invariant, then a sinusoid of infinite duration would be an eigenfunction. However, in practice, this cannot be achieved, as real signals are always time-limited. So, to mimic the infinite behavior, prefixing the end of the symbol to the beginning makes the linear convolution of the channel appear as though it were circular convolution, and thus, preserve this property in the part of the symbol after the cyclic prefix. However, there are challenges in communication systems that used cyclic prefixes in conjunction with excursion compensation.